SBI Clerk Mains Quantitative Aptitude (Day-31)

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1) A box contains 8 Pink balls, 5 black balls, 4 orange balls and 3 white balls. If four balls are drawn out randomly, then the probability of getting a different colour balls?

A) 11/35

B) 32/323

C) 18/189

D) 34/77

E) None of these

2) The ratio of the age of P after 3 years and 6 years ago, the age of Q is 3: 4. The present age of R is 2 times the present age of P. The difference between the present age of Q and R is 6 years. Find the present age of P?

A) 22 years

B) 20 years

C) 24 years

D) 16 years

E) None of these

3) The volume of cylinder 1 and 2 is in the ratio of 3: 1 and the height of the cylinder 1 and 2 is in the ratio of 3: 4. Find the ratio between the radius of cylinder 1 and cylinder 2?

A) 7: 5

B) 5: 2

C) 4: 3

D) 2: 1

E) None of these

4) The present age of Janvi and her husband is 5: 6. The present age Janvi’s daughter is (1/5) of Janvi’s present age. Janvi’s daughter is 3 years younger than her son. Find the sum of the present age of Janvi and her husband, if the age of Janvi’s son, after 7 years is 15 years?

A) 58 years

B) 66 years

C) 55 years

D) 62 years

E) None of these

5) The length of train A is 200 m and that of train B is 300 m. These two trains are running in the opposite direction with the velocities of 60 km/hr and 40 km/hr respectively. Find the time taken to cross each other?

A) 14 sec

B) 21 sec

C) 18 sec

D) 25 sec

E) None of these

6) The volume of sphere 1 and 2 is in the ratio of 27: 125. Find the ratio of the radius of sphere 1 to that of sphere 2?

A) 5: 9

B) 10: 13

C) 3: 5

D) 6: 7

E) None of these

7) Rajeev scored 412 marks in an exam and Sanjay got 75 % marks in the same exam which is 8 marks more than Rajeev. If the minimum passing marks in the exam is 35 %, then how much more marks did Rajeev score than the minimum passing marks?

A) 185

B) 172

C) 216

D) 198

E) 223

8) 200 m long train crosses another train of length 150 m in 9 sec, running in opposite direction. If the speed of the first train is 80 km/hr, then find the speed of the second train (in km/hr)?

A) 80 km/hr

B) 70 km/hr

C) 50 km/hr

D) 60 km/hr

E) None of these

9) A certain sum is divided among A, B and C in such a way that A gets 20 less than the 2/5 of the sum and B gets 1/3 of the sum and C gets Rs. 500. Find the sum?

A) Rs. 900

B) Rs. 1800

C) Rs. 2700

D) Rs. 3000

E) None of these

10) The average score of 50 students of a class is 72. If the last five students are removed, the average drops by 4 marks. If these five marks are consecutive integers, then find the least score?

A) 118

B) 106

C) 124

D) 112

E) None of these

Answers :

Directions (1-10) :

1) Answer: B

Total probability n(S) = 20C4

Required probability = n(E) = 8C1 and 5C1 and 4C1 and 3C1

P(E) = n(E)/n(S)

P(E) = (8C1 and 5C1 and 4Cand 3C1)/20C4

P(E) = 32/323

2) Answer: C

The ratio of 3 years after, the age of P and 6 years ago, the age of Q = 3: 4 (3x, 4x)

Present age of P and Q = 3x – 3, 4x + 6

The age of R = 2 * P = 2 * (3x – 3) = 6x – 6

(6x – 6) – (4x + 6) = 6

6x – 6 – 4x – 6 = 6

2x = 6 + 12

2x = 18

x = 9

Present age of P = 3x – 3 = 27 – 3 = 24 years

3) Answer: D

Volume of the cylinder = πr2h

The ratio of volume of cylinder 1 and 2 = 3: 1

The ratio of height of cylinder 1 and 2 = 3: 4

The ratio between the heights of cylinder 1 to that of cylinder 2,

= > [π * (3x) * r12]/[π * (4x) * r22] = (3/1)

= > r12/r22 = (4/1)

= > r1: r2 = 2: 1

4) Answer: C

The present age of Janvi and her husband = 5: 6 (5x, 6x)

The present age Janvi’s daughter = (1/5) * Janvi’s present age

Janvi’s daughter = Janvi’s son – 3

Janvi’s son after 7 years = 15 years

Janvi’s son’s present age = 8 years

Janvi’s daughter = 8 – 3 = 5 years

Janvi’s present age = 5 * 5 = 25 years

5’s = 25

1’s = 5

Present age of Janvi’s husband = 6x = 30 years

Required sum = 25 + 30 = 55 years

5) Answer: C

T = D/S

T = (200 + 300)/[(60 + 40) * (5/18)]

T = (500 * 18)/(100 * 5)

T = 18 sec

6) Answer: C

Volume of the sphere = (4/3) * πr3

The ratio of volume of sphere 1 and 2 = 27: 125

The ratio of the radius of sphere 1 to that of sphere 2

= > [(4/3) * π * r13]/[(4/3) * π * r23] = (27/125)

= > r13/r23 = (27/125)

= > r1: r2 = 3: 5

7) Answer: C

Let x be the total mark in that exam, then

Rajeev’s score = 412 marks, Sanjay = 75 % = Rajeev’s score – 8

Sanjay = 412 + 8 = 420 = 75 % of total marks

(75/100) * x = 420

x = 420 * (100/75) = 560

Minimum passing marks = 35 % of total marks

= > (35/100) * 560 = 196

Rajeev scored 216 marks more than the passing marks.

8) Answer: D

T = D/S

According to the question,

9 = (200 + 150)/[(80 + x) * (5/18)]

9 * [(80 + x) * (5/18)] = 350

80 + x = 140

x = 60 km/hr

9) Answer: B

Let total sum be x,

A = (2/5) * x – 20

B = (1/3) * x

C = 500

A + B + C = x

(2/5) * x – 20 + (1/3) * x + 500 = x

(11/15) * x + 480 = x

480 = x – (11/15) * x

(4/15) * x = 480

x = 480 * (15/4) = Rs. 1800

10) Answer: B

The average score of 50 students = 72

Total score of 50 students = 50 * 72 = 3600

If the last five students are removed, the average drops by 4 marks.

So,

The average score of 45 students = 68

Total score of 45 students = 45 * 68 = 3060

x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 540

5x + 10 = 540

5x = 530

x = 106

Least score = 106

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